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The fair allocation of resources to agents is a fundamental problem in society and has received significant attention and rapid developments from the game theory and artificial intelligence communities in recent years. The majority of the fair division literature can be divided along at least two orthogonal directions: goods versus chores, and divisible versus indivisible resources. In this survey, besides describing the state of the art, we outline a number of interesting open questions in three mixed fair division settings: (i) indivisible goods and chores, (ii) divisible and indivisible goods (i.e., mixed goods), and (iii) fair division of indivisible goods with subsidy.